Not really mathy, but some outlook from Ask Mr Robot(yes, this gets posted everywhere, I know I know):
My Point being, that grinding it is not "worth" it, since it's exponentiell more AP you need. Only with higher AK it gets better. This is no accident, Blizzard wants you to keep subbed
.
Just do your daily hc, all the WQs, the occasional mythic+, lfr and normal/hc Raids, and you'll have an 34 Artifact around December, and the full maxed 54 around March.
Even grinding hc's and m+'s nonstop won't get there considerably faster, maybe some days at most. IMHO, not worth it - AK is just too powerful, and the deciding factor.